3/2p-14=p+14

Solution for 3/2p-14=p+14 equation:

3/2p-14=p+14

We move all terms to the left:

3/2p-14-(p+14)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

3/2p-p-14-14=0

We multiply all the terms by the denominator


-p*2p-14*2p-14*2p+3=0

Wy multiply elements

-2p^2-28p-28p+3=0

We add all the numbers together, and all the variables

-2p^2-56p+3=0

a = -2; b = -56; c = +3;
Δ = b2-4ac
Δ = -562-4·(-2)·3
Δ = 3160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{790}}{2*-2}=\frac{56-2\sqrt{790}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{790}}{2*-2}=\frac{56+2\sqrt{790}}{-4}
$